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__Hydraulics_of_Spillways_and_Energy_Dissipators__Civil_and_Environmental_Engineering_.pdf
Hydraulics of
Spillways and
Energy Dissipators
DK1222_half-series-title 9/15/04 1:13 PM Page 1
Civil and Environmental Engineering
A Series of Reference Books and Textbooks
Editor
Michael D. Meyer
Department of Civil and Environmental Engineering
Georgia Institute of Technology
Atlanta, Georgia
1. Preliminary Design of Bridges for Architects and Engineers
Michele Melaragno
2. Concrete Formwork Systems
Awad S. Hanna
3. Multilayered Aquifer Systems: Fundamentals and Applications
Alexander H.-D. Cheng
4. Matrix Analysis of Structural Dynamics: Applications
and Earthquake Engineering
Franklin Y. Cheng
5. Hazardous Gases Underground: Applications to Tunnel Engineering
Barry R. Doyle
6. Cold-Formed Steel Structures to the AISI Specification
Gregory J. Hancock, Thomas M. Murray, Duane S. Ellifritt
7. Fundamentals of Infrastructure Engineering: Civil Engineering Systems:
Second Edition, Revised and Expanded
Patrick H. McDonald
8. Handbook of Pollution Control and Waste Minimization
Abbas Ghassemi
9. Introduction to Approximate Solution Techniques, Numerical Modeling,
and Finite Element Methods
Victor N. Kaliakin
10. Geotechnical Engineering: Principles and Practices of Soil Mechanics
and Foundation Engineering
V
. N. S. Murthy
Additional Volumes in Production
Chemical Grouting and Soil Stabilization: Third Edition,
Revised and Expanded
Reuben H. Karol
Estimating Building Costs
Calin M. Popescu, Kan Phaobunjong, Nuntapong Ovararin
DK1222_half-series-title 9/15/04 1:13 PM Page 2
Marcel Dekker New York
R. M. Khatsuria
Hydraulics of
Spillways and
Energy Dissipators
DK1222_half-series-title 9/15/04 1:13 PM Page 3
Although great care has been taken to provide accurate and current information, neither
the author(s) nor the publisher, nor anyone else associated with this publication, shall be
liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused
by this book. The material contained herein is not intended to provide specific advice or
recommendations for any specific situation.
Trademark notice: Product or corporate names may be trademarks or registered trademarks
and are used only for identification and explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress.
ISBN: 0-8247-5789-0
This book is printed on acid-free paper.
Headquarters
Marcel Dekker, 270 Madison Avenue, New York, NY 10016, U.S.A.
tel: 212-696-9000; fax: 212-685-4540
Distribution and Customer Service
Marcel Dekker, Cimarron Road, Monticello, New York 12701, U.S.A.
tel: 800-228-1160; fax: 845-796-1772
World Wide Web
http://www.dekker.com
Copyright  2005 by Marcel Dekker. All Rights Reserved.
Neither this book nor any part may be reproduced or transmitted in any form or by any
means, electronic or mechanical, including photocopying, microfilming, and recording,
or by any information storage and retrieval system, without permission in writing from
the publisher.
Current printing (last digit):
10 9 8 7 6 5 4 3 2 1
PRINTED IN THE UNITED STATES OF AMERICA
To My Parents
Ad

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__Hydraulics_of_Spillways_and_Energy_Dissipators__Civil_and_Environmental_Engineering_.pdf

  • 2. Hydraulics of Spillways and Energy Dissipators DK1222_half-series-title 9/15/04 1:13 PM Page 1
  • 3. Civil and Environmental Engineering A Series of Reference Books and Textbooks Editor Michael D. Meyer Department of Civil and Environmental Engineering Georgia Institute of Technology Atlanta, Georgia 1. Preliminary Design of Bridges for Architects and Engineers Michele Melaragno 2. Concrete Formwork Systems Awad S. Hanna 3. Multilayered Aquifer Systems: Fundamentals and Applications Alexander H.-D. Cheng 4. Matrix Analysis of Structural Dynamics: Applications and Earthquake Engineering Franklin Y. Cheng 5. Hazardous Gases Underground: Applications to Tunnel Engineering Barry R. Doyle 6. Cold-Formed Steel Structures to the AISI Specification Gregory J. Hancock, Thomas M. Murray, Duane S. Ellifritt 7. Fundamentals of Infrastructure Engineering: Civil Engineering Systems: Second Edition, Revised and Expanded Patrick H. McDonald 8. Handbook of Pollution Control and Waste Minimization Abbas Ghassemi 9. Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods Victor N. Kaliakin 10. Geotechnical Engineering: Principles and Practices of Soil Mechanics and Foundation Engineering V . N. S. Murthy Additional Volumes in Production Chemical Grouting and Soil Stabilization: Third Edition, Revised and Expanded Reuben H. Karol Estimating Building Costs Calin M. Popescu, Kan Phaobunjong, Nuntapong Ovararin DK1222_half-series-title 9/15/04 1:13 PM Page 2
  • 4. Marcel Dekker New York R. M. Khatsuria Hydraulics of Spillways and Energy Dissipators DK1222_half-series-title 9/15/04 1:13 PM Page 3
  • 5. Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recommendations for any specific situation. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-5789-0 This book is printed on acid-free paper. Headquarters Marcel Dekker, 270 Madison Avenue, New York, NY 10016, U.S.A. tel: 212-696-9000; fax: 212-685-4540 Distribution and Customer Service Marcel Dekker, Cimarron Road, Monticello, New York 12701, U.S.A. tel: 800-228-1160; fax: 845-796-1772 World Wide Web http://www.dekker.com Copyright  2005 by Marcel Dekker. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA
  • 8. Preface The need for a comprehensive book dealing in hydraulics of spillways and energy dissipators has been realized since long. Various topics pertaining to the spillways and energy dissipators are available in the sources devoted mainly to the design of dams, text books on hydraulics and open channel flow and handbooks of hydraulics. However, advances in research and design, generally published through papers presented at the specialty conferences and journals, are seldom disseminated wide enough for application on a general scale. Consequently, the rift between the advancements in knowledge and its formal documentation in the books and treatise grows wider. Of the many examples illustrating this lag, a typical one is the aerator on spillways to mitigate cavitation damage. Although, the beneficial effects of aeration were known in the early fifties, considerable research had been pursued, to understand hydraulics of the phenomenon, from the sixties and aeration devices were installed on the existing structures in the late seventies, it was not until the eighties that aeration devices became an integral part of spillway design. It is noteworthy that no book on spillways published until the late eighties included the topic of aeration, and reference sources re- mained scattered in journals and proceedings. This practice of lag continues, as several topics of vital significance have not been embodied comprehensively and coherently into any of the book literature. A few to mention include: spillway construction stages, spillways serving dual pur- pose of flood as well as sediment disposal, overtopping protection of earth dams used as spillways, prediction of and protection against detrimental forces such as uplift, cavitation, scour etc. It is obvious that such a book would be the easiest way for a reader to access the information on the latest developments in the field. The present book is the outcome of such an attempt. The book has been organized into four sections dealing with spillways, energy dissipators, cavitation and air entrainment, and hydraulic modeling. Em- phasis has been on discussing first the hydraulics of different types of spillways and energy dissipators and to illustrate its application to practical design problems. To this end, illustrative examples have been included at appropriate places. v
  • 9. Preface vi The first two chapters in section I introduce the topic and broad design philosophy. The chapter on spillway design flood defines two distinct aspects: the estimation, which is hydrologist’s regime and the selection, which is the responsibility of the designer. Subsequent chapters have been devoted to discus- sion on hydraulics and general design features of different types of spillways such as ogee, chute and side channel, stepped, siphon, shaft, tunnel, labyrinth and duck bill, free jet and fuse plug etc. Special features such as spillways for flood and sediment disposal, inflatable rubber weirs and overtopping protection of dams used as spillways have also been included. Separate chapters on spillway crest gates and spillway construction stages have been written. Discussions on the three most common types of energy dissipators for spillways, viz. hydraulic jump stilling basins, trajectory buckets and submerged roller buckets in section II, have been quite elaborate, obviously in view of the large amount of information published during recent years. Energy dissipators for shaft and tunnel spillways warrant a special chapter in view of peculiar hydraulic conditions at the outfalls. Separate chapters have been devoted to the discussion of impact type energy dissipators and some unconventional or special designs of energy dissipators. Section III includes chapters on the topics of cavitation and air entrainment and aerators concerning the design of spillways and energy dissipators. Hydraulic modeling of spillways and energy dissipators has been covered in section IV. No attempt has been made to discuss the theory of similitude and hydraulic models, found in many books. On the other hand, emphasis has been placed on topics of scale effect; dynamic flow measurement and aspects of analy- sis and interpretation of model results. It is hoped that this will be useful, to not only research engineers, but also to the designers and practicing engineers direct- ing the model studies. In the field of technology, a continuous stream of development and improve- ment adds to the knowledge. Therefore, nothing can be claimed as exhaustive or final. Similarly, it is equally difficult to decide what is old or obsolete. The difficult task was therefore to evaluate every piece of information from the stand- point of practical utility, be it for the researcher, designer, practicing engineer or student. While this book is not intended to be a textbook to cater to any specific curriculum, nor a handbook, it is expected to serve as a comprehensive reference source for all concerned. It is hoped that the reader will be able to obtain an extensive exposure of the topic, beyond which the references listed at the end of the chapters will be useful for locating additional details. Experience gained during my association, of nearly four decades, with the Central Water and Power Research Station, Pune—an institution of international reputation and discussions with several experts in the field of their own specialist knowledge, have greatly contributed to writing of the book. Thanks are also due to friends and colleagues for their help and encouragement which lent a strong
  • 10. Preface vii impetus toward the completion of this book. My wife Kala, daughters Pallavi, Reshma, and son-in-law Praveen extended support throughout the writing of the book. I have pleasure in placing on record, my appreciation for the excellent coordination by Mr. B.J. Clark, Executive Acquisitions Editor, Mr. E.F. Stannard, Senior Production Editor and Ms. Kerry Doyle, Director, Book Editorial, Marcel Dekker, Inc. at various stages of publication of the book. Feedback from the readers in respect of any omission or error as also their comments and suggestions to improve upon the contents of the book, shall be gratefully appreciated. R. M. Khatsuria 5/4, Krutarth Society Behind Sharda Bank Off: Satara Road, PUNE - 411 037, INDIA Email - rmkhatsuria@rediffmail.com
  • 12. Acknowledgments The author acknowledges with thanks, the following institutions, organizations and individuals who permitted to refer/reproduce their publications in this book. The details of the materials have been listed in the appropriate reference sections within the chapters. – American Society of Civil Engineers, New York, USA – Aqua-Media International Ltd, UK (Jnl of Hydropower and Dams) – Bacchiega, J.D, Fattor, C.A and Barrionuevo, H.C (INA, Argentina) – Back, Paul, Berks, UK – BHR Group Limited, Cranfield, UK – Canadian Society of Civil Engineers, Canada – Central Board of Irrigation and Power (CBIP), New Delhi, India – Chanson, H (The University of Queensland, Australia) – Damulevicius, V and Ruplys, B (LZUU, Lithuania) – Ervine, D.A. (The University of Glasgow, UK) – Gao, JiZhang, IWHR, Beijing, China – Hager, W.H., ETH, Switzerland – Iguacel, C.M, CEDEX, Spain – Indian Institute of Science, Bangalore, India – Indian Society for Hydraulics, Pune, India – Institution of Civil Engineers, London, UK – Institution of Engineers Australia, Melbourne, (XXI IAHR 1985) – Institution of Engineers (India), Kolkata, India – International Association for Hydraulic Research, (IAHR), Madrid, Spain (Jnl of Hyd Res, VI–VII IAHR, 1955, 1957) – International Congress on Large dams (ICOLD), Paris, France (ICOLD Publications) – Japan Society of Civil Engineers, Tokyo, Japan – Jongeling, T (Delft Hydraulics), The Netherlands – National Hydroelectric Power Corporation Ltd, New Delhi, India ix
  • 13. Acknowledgments x – National University of Singapore (IX APD-IAHR, 1994) – Rathgeb, A (Wasser-und Schiffahrtsamt, Stuttgart), Germany – SAF Laboratory, University of Minnesota, USA – Sardar Sarovar Narmada Nigam Ltd (SSNNL), Gandhinagar, India – Schleiss, A, EPFL, Switzerland (XXII IAHR 1987) – Swets and Zeitlinger Publishers, (Balkema Publishers), The Netherlands – Technische Akademie Esslingen (TAE), Germany (IAHR Symp 1984) – Thomas Telford Publishing, London, UK (XXVI IAHR 1995) – Plate, E, University of Karlsruhe, Germany (XVII IAHR 1977) – United States Army Corps of Engineers (USACE), USA – UNESCO Publishing, Paris, France – United States Bureau of Reclamation (USBR), USA – United States Society on Dams (USCOLD), USA – Virginia Polytechnic Institute, USA – Wang, Lianxiang IWHR, China (XXIX IAHR 2001) – Wilmington Publishing, Kent, UK (Jnl of Water Power and Dam Con- struction) – Wilmington Publishing, Kent, UK (Dam Engineering) – Yugoslav Association for Hydraulic Research (YAHR), Belgrade, Serbia – Yasuda, Y (Nihon University), Japan
  • 14. Contents Preface .......................................................................................................... v Acknowledgments ......................................................................................... ix Section I: Spillways 1. Spillways: Functions and Classification ............................................. 1 1.1. Introduction ............................................................................. 1 1.2. Necessity of a spillway ........................................................... 1 1.3. Functions of a spillway ........................................................... 2 1.4. Classification of spillways ...................................................... 5 2. Spillway Design: An Overview .......................................................... 7 2.1. Introduction ............................................................................. 7 2.2. Analysis of existing structures ................................................ 7 2.3. Various aspects involved in a spillway design ...................... 9 2.3.1. Hydrology .................................................................... 9 2.3.2. Topography and geology ............................................ 10 2.3.3. Utility and operational aspects ................................... 10 2.3.4. Constructional and structural aspects ......................... 12 2.4. Economic analysis ................................................................... 13 3. Spillway Design Flood: Estimation and Selection ............................. 15 3.1. Introduction ............................................................................. 15 3.2. Estimation of spillway design flood ....................................... 16 3.3. Methods based mainly on flow data ...................................... 16 3.3.1. Historical method ........................................................ 16 3.3.2. Empirical and regional formulas ................................ 17 3.3.3. Envelope curves .......................................................... 17 3.3.4. Flood frequency analysis ............................................ 18 xi
  • 15. Contents xii 3.4. Methods based mainly on rainfall data .................................. 19 3.4.1. Development of the PMS and PMP ........................... 20 3.4.2. Unit hydrograph method ............................................. 22 3.4.3. Hydrologic modelling ................................................. 22 3.4.4. Gradex method ............................................................ 24 3.5. Flood estimation methods: Critical analysis .......................... 24 3.5.1. Estimation of design flood for the Sardar Sarovar Dam on River Narmada, India ................................... 25 3.6. Selection of spillway design flood ......................................... 27 3.6.1. Economic risk analysis (ERA) ................................... 28 3.6.2. Comments on ERA ..................................................... 29 3.6.3. Design flood standards and regulations ..................... 30 3.6.4. Comments on design standards .................................. 34 3.6.5. Quantitative risk assessment ....................................... 34 3.6.6. Incremental hazard evaluation .................................... 35 4. Ogee or Overflow Spillways ............................................................... 41 4.1. Introduction ............................................................................. 41 4.2. The spillway crest profile ....................................................... 41 4.3. Discharge characteristics ......................................................... 48 4.4. Discharge coefficient versus crest pressures .......................... 55 4.5. Determination of design head ................................................. 57 4.6. Crest piers ................................................................................ 59 4.7. Downstream slope or rear slope ............................................. 59 4.8. Water surface profile ............................................................... 59 4.9. Spillway toe ............................................................................. 60 5. Chute and Side Channel Spillways ..................................................... 63 5.1. Introduction ............................................................................. 63 5.2. Principal elements ................................................................... 64 5.3. Approach channel .................................................................... 64 5.4. Spillway structure .................................................................... 67 5.5. Side channel spillway-trough and control section ................. 69 5.6. Chute ........................................................................................ 78 5.6.1. Contraction and Expansion ......................................... 79 5.6.2. Curvature in plan ........................................................ 86 5.6.3. Special layouts ............................................................ 89 5.6.4. Longitudinal profiles ................................................... 89 5.6.5. Tail channel ................................................................. 91 5.7. Numerical and physical modeling .......................................... 91 6. Stepped Spillways ............................................................................... 95 6.1. Introduction ............................................................................. 95
  • 16. Contents xiii 6.2. Historical background ............................................................. 95 6.3. Flow regimes on a stepped chute ........................................... 95 6.4. Characteristics of the nappe flow ........................................... 96 6.4.1. Nappe flow occurrence ............................................... 98 6.4.2. Energy dissipation and residual head for nappe flow 98 6.4.3. Pooled step cascades ................................................... 101 6.4.4. Transition flow regime ............................................... 105 6.5. Characteristics of the skimming flow ..................................... 106 6.5.1. Estimation of flow resistance ..................................... 107 6.5.2. Air entrainment ........................................................... 110 6.5.3. Energy dissipation ....................................................... 114 6.5.4. Pressure fluctuations and cavitation susceptibility .... 121 6.6. Guidelines for design of stepped spillways ............................ 122 6.6.1. Crest profile and the transition ................................... 122 6.6.2. Step height ................................................................... 123 6.6.3. Freeboard for sidewalls ............................................... 124 6.6.4. Design of energy dissipator ........................................ 124 6.7. Hydraulic model studies ......................................................... 124 7. Siphon Spillways ................................................................................. 129 7.1. Introduction ............................................................................. 129 7.2. Types of siphon ....................................................................... 129 7.3. Hydraulic action ...................................................................... 131 7.4. Hydraulic design considerations ............................................. 133 7.5. Discharging capacity ............................................................... 134 7.6. Priming depth .......................................................................... 140 7.7. Flow regulation ....................................................................... 141 7.8. Stability of functioning ........................................................... 143 7.9. Effect of waves ....................................................................... 143 7.10. Cavitation ................................................................................ 143 7.11. Vibration .................................................................................. 147 8. Shaft Spillways .................................................................................... 151 8.1. Introduction ............................................................................. 151 8.2. Types of shaft spillways ......................................................... 151 8.3. Shaft spillways with axial flow .............................................. 152 8.3.1. Hydraulic action .......................................................... 154 8.3.2. Analysis of alternatives ............................................... 154 8.4. Free shaft spillways ................................................................. 156 8.4.1. Crest profile ................................................................. 157 8.4.2. Transition from crest to shaft ..................................... 159
  • 17. Contents xiv 8.4.3. Discharge characteristics ............................................. 160 8.4.4. Air entrainment in drop shafts .................................... 162 8.4.5. Air entrainment in tunnels flowing partly full ........... 171 8.5. Pressure shaft spillways .......................................................... 172 8.5.1. Devices to ensure pressurized flow in the shaft ........ 173 8.5.2. Release of air in pressurized tunnels .......................... 174 8.6. The vortex drop ....................................................................... 179 8.6.1. Configuration of vortex-flow intakes ......................... 181 8.6.2. Standard scroll intake ................................................. 181 8.6.3. Tangential vortex intake ............................................. 186 8.6.4. Designs of drop shafts to increase discharge capacity ........................................................................ 188 8.6.5. Air entrainment and transport in vortex drops ........... 188 8.7. Shaft spillways with swirling flow in outlet tunnel ............... 190 8.8. Siphon-shaft spillway .............................................................. 192 9. Labyrinth and Duckbill Spillways ...................................................... 197 9.1. Introduction ............................................................................. 197 9.2. General characteristics of labyrinth weirs .............................. 197 9.3. Parameters affecting performance .......................................... 199 9.4. Discharge characteristics ......................................................... 202 9.5. Design of labyrinth spillway ................................................... 207 9.6. Duckbill spillway .................................................................... 209 9.7. Designs relevant to existing and new structures .................... 213 10. Tunnel and Culvert Spillways ............................................................. 217 10.1. Introduction ............................................................................. 217 10.2. Tunnel spillways: Design considerations ............................... 217 10.2.1. Control structure ......................................................... 217 10.2.2. Discharge tunnel ......................................................... 220 10.2.3. Other forms of discharge tunnels ............................... 222 10.3. Culvert spillway ...................................................................... 223 10.3.1. Full bore flow (Pipe culverts) .................................... 225 10.3.2. Box and MEL culverts ................................................ 226 10.4. Conduit pressures .................................................................... 227 11. Free Jet and Straight Drop Spillways ................................................. 231 11.1. Introduction ............................................................................. 231 11.2. Free jet spillways: Design considerations .............................. 231 11.2.1. Overflow crest ............................................................. 232 11.2.2. Stilling basin ............................................................... 232
  • 18. Contents xv 11.3. Characteristics of the free falling jets .................................... 232 11.4. Guidelines for the design of a stilling basin .......................... 241 11.5. Nappe splitters and dispersers ................................................ 244 11.6. Bottom outlets: Design considerations ................................... 248 11.7. Straight drop spillway ............................................................. 254 12. Fuse Plugs and Fuse Gate Spillways .................................................. 261 12.1. Introduction ............................................................................. 261 12.2. Fuse plug ................................................................................. 261 12.2.1. Criteria for selection of fuse plug .............................. 262 12.2.2. Design considerations ................................................. 262 12.2.3. Providing a fuse plug in an existing dam .................. 266 12.2.4. Hydraulics of flood discharge through fuse plug opening ........................................................................ 266 12.3. Fuse gates ................................................................................ 269 12.3.1. Functioning of fuse gates ............................................ 269 12.3.2. Stability of fuse gates ................................................. 271 12.3.3. Design of fuse gates .................................................... 274 12.3.4. Recoverable fuse gates ............................................... 280 13. Spillways for Flood and Sediment Disposal ...................................... 283 13.1. Introduction ............................................................................. 283 13.2. Reservoir sedimentation and flushing .................................... 283 13.3. Alternatives available .............................................................. 284 13.4. Flushing discharge .................................................................. 284 13.5. Gated overflow spillway ......................................................... 285 13.6. Orifice spillways ..................................................................... 286 13.7. Bottom outlets ......................................................................... 286 13.8. Design considerations ............................................................. 288 13.8.1. Discharge characteristics of spillway ......................... 288 13.8.2. Waterway of the structures ......................................... 289 13.8.3. Size and dimensions of structures .............................. 289 13.8.4. Energy dissipator ......................................................... 293 13.8.5. Power intakes .............................................................. 295 13.8.6. Gates ............................................................................ 295 13.8.7. Protection of flow surfaces ......................................... 296 13.9. Mathematical and physical model studies .............................. 297 14. Unlined Spillways ............................................................................... 299 14.1. Introduction ............................................................................. 299 14.2. Unlined rock spillways ........................................................... 299 14.3. Unlined cascade spillways ...................................................... 300
  • 19. Contents xvi 14.4. General considerations ............................................................ 300 14.5. Conceptual framework ............................................................ 301 14.6. Rock-fill spillways .................................................................. 307 15. Inflatable Rubber Weirs ...................................................................... 313 15.1. Introduction ............................................................................. 313 15.2. Principal elements of a rubber weir ....................................... 313 15.3. Design considerations ............................................................. 315 15.3.1. Hydraulic design ......................................................... 315 15.3.2. Structural design ......................................................... 320 15.4. Problems associated with rubber weir installation ................. 321 16. Overtopping Protection of Dams Used as Spillways ......................... 323 16.1. Introduction ............................................................................. 323 16.2. Concrete dam overtopping protection .................................... 323 16.3. Embankment dam overtopping protection ............................. 325 16.4. Design considerations ............................................................. 325 16.5. Slope protection lining ............................................................ 327 16.5.1. Cast-in-place concrete ................................................. 327 16.5.2. Roller compacted concrete (RCC) .............................. 327 16.5.3. Precast concrete block system .................................... 328 17. Spillway Crest Gates ........................................................................... 333 17.1. Introduction ............................................................................. 333 17.2. Factors influencing the decision ............................................. 333 17.2.1. Safety of the dam ........................................................ 334 17.2.2. Cost economics ........................................................... 334 17.2.3. Operational problems .................................................. 335 17.2.4. Downstream conditions ............................................... 335 17.2.5. Special considerations ................................................. 335 17.3. Types of gates ......................................................................... 336 17.4. Mechanical gates ..................................................................... 337 17.4.1. Radial gates ................................................................. 337 17.4.2. Vertical lift gates ......................................................... 343 17.4.3. Flap gates .................................................................... 345 17.5. Semi-mechanical gates ............................................................ 346 17.6. Automatic type: fusible ........................................................... 346 17.7. Automatic type: restoring ....................................................... 346 17.8. Vibration of gates .................................................................... 350 17.9. Stop log gates .......................................................................... 350 17.10. Some considerations on operating pattern of gates ............... 355
  • 20. Contents xvii 18. Spillway Construction Stages ............................................................. 359 18.1. Introduction ............................................................................. 359 18.2. Spillway construction program ............................................... 359 18.3. Construction flood ................................................................... 360 18.4. Reservoir levels during construction stages ........................... 360 18.5. Spillway construction stages ................................................... 361 18.5.1. Discharge characteristics of partly constructed spillways ...................................................................... 364 18.6. Flow downstream of partly constructed spillways ................. 366 Section II: Energy Dissipators 19. Energy Dissipators for Spillways ....................................................... 371 19.1. Introduction ............................................................................. 371 19.2. Classification of energy dissipators ........................................ 371 19.3. Principal types of energy dissipators ...................................... 372 19.4. Selection of the type of energy dissipator .............................. 373 19.5. Analysis of Parameters ........................................................... 375 20. Hydraulic Jump Stilling Basins .......................................................... 387 20.1. Introduction ............................................................................. 387 20.2. Hydraulic jump characteristics ............................................... 387 20.2.1. Classification of hydraulic jump ................................ 388 20.2.2. Length of the jump ..................................................... 390 20.2.3. Conjugate depth and energy loss ................................ 390 20.2.4. Turbulence characteristics of hydraulic jump ............ 392 20.2.5. Air entrainment by hydraulic jump ............................ 399 20.3. Hydraulic jump stilling basins ................................................ 401 20.3.1. Basins with horizontal aprons .................................... 401 20.3.2. Basins with sloping aprons ......................................... 409 20.4. Optimization of designs .......................................................... 411 20.5. Structural design problems ..................................................... 411 20.5.1. Uplift ........................................................................... 411 20.5.2. Hydrodynamic forces .................................................. 423 20.5.3. Cavitation .................................................................... 428 20.5.4. Vibrations .................................................................... 431 20.5.5. Abrasion ...................................................................... 432 20.6. Environmental considerations ................................................. 433 20.7. Implications of various factors ............................................... 434
  • 21. Contents xviii 21. Trajectory Buckets .............................................................................. 441 21.1. Introduction ............................................................................. 441 21.2. Types and classification .......................................................... 441 21.3. Design of bucket components ................................................. 443 21.3.1. Shape of the bucket .................................................... 444 21.3.2. Invert elevation ........................................................... 445 21.3.3. Bucket radius ............................................................... 445 21.3.4. Lip angle ..................................................................... 446 21.4. Hydraulic characteristics of trajectory buckets ...................... 448 21.4.1. Pressures on buckets and sidewall ............................. 449 21.4.2. Free trajectory and throw ............................................ 453 21.4.3. Effect of submergence by tail water .......................... 455 21.5. Scour downstream of trajectory buckets ................................ 465 21.5.1. Computation and prediction ....................................... 465 21.5.2. Analysis ....................................................................... 469 21.5.3. Scour control and remedial measures ........................ 470 21.5.4. Protection against scour .............................................. 471 21.6. Special forms of buckets ......................................................... 472 22. Solid and Slotted Roller Buckets ........................................................ 483 22.1. Introduction ............................................................................. 483 22.2. Solid roller bucket ................................................................... 483 22.3. Slotted roller bucket ................................................................ 491 22.4. Comparative performance based on prototype experience .... 495 22.5. Alternative designs for improvements .................................... 499 23. Energy Dissipators for Shaft and Tunnel Spillways .......................... 503 23.1. Introduction ............................................................................. 503 23.2. Full-bore pressurized flow ...................................................... 503 23.2.1. Dissipation by friction ................................................ 505 23.2.2. Dissipation by head loss ............................................. 505 23.2.3. Swirling devices .......................................................... 505 23.3. Free surface flow ..................................................................... 507 23.3.1. Flip buckets ................................................................. 507 23.3.2. Hydraulic jump stilling basin ..................................... 509 24. Impact-Type Energy Dissipators ......................................................... 519 24.1. Introduction ............................................................................. 519 24.2. Classification of impact-type energy dissipators .................... 519 24.3. Baffled chutes .......................................................................... 520 24.3.1. Energy dissipation by induced tumbling flow ........... 520 24.3.2. Baffled apron drops .................................................... 522
  • 22. Contents xix 24.4. Energy dissipators for spillways and outlets .......................... 524 24.4.1. USER Basin VI ........................................................... 524 24.4.2. Bhavani-type stilling basin ......................................... 526 25. Unconventional Designs ...................................................................... 531 25.1. Introduction ............................................................................. 531 25.2. Dissipating part of the energy on a spillway slope ................ 531 25.3. Interaction within the region of flow ..................................... 532 25.4. Bifurcation/bypass of flow ...................................................... 535 25.5. Hydraulic model studies ......................................................... 538 Section III: Cavitation and Air Entrainment 26. Cavitation in Spillways and Energy Dissipators ................................ 541 26.1. Introduction ............................................................................. 541 26.2. Cavitation ................................................................................ 541 26.3. Cavitation index ...................................................................... 542 26.4. Cavitation damage ................................................................... 544 26.5. Cavitation on spillway surfaces .............................................. 545 26.5.1. Inadequate design ........................................................ 546 26.5.2. Misalignment ............................................................... 547 26.5.3. Surface roughness ....................................................... 548 26.6. Cavitation in energy dissipators ............................................. 550 26.6.1. Fluctuating pressure depressions ................................ 552 26.6.2. Flow separation and reattachment .............................. 553 26.7. Cavitation due to sheared flow and vortices .......................... 556 26.8. Prediction of cavitation damage ............................................. 560 26.9. Prevention of cavitation in spillways and energy dissipators 562 26.9.1. Design .......................................................................... 562 26.9.2. Construction ................................................................ 563 26.9.3. Operation of structures ............................................... 564 26.l0. Remedial measures and repairs .............................................. 564 27. Air Entrainment and Forced Aeration ................................................ 569 27.1. Introduction ............................................................................. 569 27.2. Air entrainment on spillways .................................................. 569 27.3. Location of point of inception ................................................ 572 27.4. Properties of aerated flow ....................................................... 579 27.5. The region of varied flow ....................................................... 584 27.6. Effect of entrained air on stilling basin performance ............ 586 27.7. Forced aeration ........................................................................ 586
  • 23. Contents xx 27.8. Mechanism of aeration ............................................................ 587 27.9. Design of an aerator system ................................................... 590 27.9.1. Location of the aerator ................................................ 590 27.9.2. Types of aerators ......................................................... 591 27.9.3. Volume of air entrained by an aerator ....................... 591 27.9.4. Air supply systems ...................................................... 596 27.9.5. Aerator spacing ........................................................... 597 27.10. Aerators for tunnel spillways and outlets ............................... 601 27.11. Aerators on existing structures ............................................... 604 Section IV: Hydraulic Modeling 28. Hydraulic Modeling of Spillways and Energy Dissipators ................ 609 28.1. Introduction ............................................................................. 609 28.2. A review of dimensionless numbers ...................................... 609 28.3. Hydraulic modeling and scale effect ...................................... 611 28.3.1. Friction ........................................................................ 611 28.3.2. Turbulence ................................................................... 615 28.3.3. Cavitation .................................................................... 617 28.3.4. Air entrainment and release ........................................ 617 28.3.5. Fluid-structure interaction ........................................... 621 28.4. Dynamic-flow measurement ................................................... 624 28.4.1. Measurement ............................................................... 624 28.4.2. Analysis of results ....................................................... 627 28.4.3. Interpretation of results ............................................... 629 Index ............................................................................................................. 637
  • 24. 1 Spillways: Functions and Classification 1.1 INTRODUCTION ‘‘He who creates a potential danger is responsible for doing everything within human power to control it.’’ The function of a spillway can be best illustrated as emanating from the above well-known legal argument. Impounding large quantity of water behind a dam creates the danger of a dam-break flood wave, which could have catastrophic consequences. The safe design of a dam to avoid such a danger includes a spill- way, aptly described as the safety valve of the dam-reservoir system. 1.2 NECESSITY OF A SPILLWAY A spillway is designed to prevent overtopping of a dam at a place that is not designed for overtopping. Vischer et al. (1988) discuss the necessity of a spillway with reference to the following questions: Is overflowing of the reservoir possible? Could overtopping cause a dam failure? Could overtopping cause any other damage? A reservoir will overflow if its capacity is less than the difference between the volumes of inflow and outflow. If a dam can, economically, be made high enough to provide a retention space above Full Supply Level (FSL) to absorb the entire volume of inflow design flood, no spillway would be required and an outlet such as a turbine or sluice would only be needed for regulating/utilizing storage. There are indeed a few dams where spillways were dispensable or a nominal spillway facility was all that was needed; Moric (1997) has reported two such cases. However, in a majority of cases, it is impractical to provide retention capacity 1
  • 25. Chapter 1 2 above FSL large enough to absorb the inflow design flood and, hence, a special device to surplus the extra quantity of water is required, namely a spillway. Whether a dam would fail due to overtopping depends largely on the type of the dam in question. The most sensitive structures are earth-fill dams, which—if not specially protected—are destroyed by even a small overtopping. Masonry and concrete dams, as well as gravity and arch dams can withstand overtopping up to certain extent before they fail due to excessive stresses. However, the indirect threat to their stability due to erosion from an immediate downstream, mainly by overflowing impinging jet, would be of more concern. Overtopping of a dam may also cause other damages to the nearby structures that are not designed for such overtopping. Considering the above, one can conclude that all dams should be constructed with a safety device, in the form of a spillway, against overtopping. The question then arises as to what portion of the total cost of the dam a spillway constitutes. The available information indicates a large variation, ranging from 4% (unlined rock spillways) to 22% (spillways for earth and rock-fill dams). Generally, spill- ways account for a small portion of the cost in concrete and arch dams as compared to those with earth or rock-fill dams. However, it seems more appropriate to consider the cost of a spillway in terms of each cumec released rather than the cost of the complete spillway structure in relation to the total cost of the dam. A pertinent observation in this regard is provided by Mriouah (1988), of the spillway of Oued el Makhazine dam (Morocco), where increasing the design flood 2.5 times from 3500 to 8600 cumec (dam height increased by 0.5 m) raised the overall cost of the structure by only 3%. This issue can also be considered in terms of dam safety. A United States Bureau of Reclamation (USBR) report (1983) states that spillway inadequacy represents about 40% of the dam failure hazards. Compared with this figure, the percentage cost of the spillway, especially from the standpoint of marginal cost, is usually much lower. 1.3 FUNCTIONS OF A SPILLWAY While the principal function of a spillway is to pass down the surplus water from the reservoir into the downstream river, there are precisely seven functions that can be assigned to spillway as discussed by Takasu et al. (1988). 1. Maintaining normal river water functions (compensation water supply) 2. Discharging water for utilization 3. Maintaining initial water level in the flood-control operation 4. Controlling floods 5. Controlling additional floods
  • 26. Spillways: Functions and Classification 3 6. Releasing surplus water (securing dam and reservoir safety) 7. Lowering water levels (depleting water levels in an emergency) It may be mentioned that the above functions have been defined for spillways and regulating outlets as per the Cabinet Orders Concerning Structural Criteria for River Administration Facilities and have been applied to all dams constructed in Japan. Part of the function under (1), (2), and (3) are combined with outlets for low water. Facilities providing function (5) are added to (4) or (6) and are collectively called outlets for high water. Function (7) is essentially for reservoir depletion, which is generally accomplished by low-level outlets. Figure 1 shows graphically the above functions in water level–discharge domain. Figure 1 Functions of Spillways and Regulating Outlets. (Takasu et al.-1988) A: Design flood level, B: Surcharge level, C: Initial water level in flood-control operation, D: Mini- mum operating level, a: Maximum outflow for water supply, b: Initial inflow discharge in the flood-control operation, c: Maximum outflow discharge in the flood-control opera- tion, d: Standard project flood discharge, e: Spillway design flood discharge, 1: Mainte- nance of normal river water functions (compensation water), 2: Discharge for water utiliza- tion, 3: Maintaining initial water level in flood-control operation, 4: Flood control, 5: Additional flood control, 6: Release of surplus water.
  • 27. Chapter 1 4 Figure 2 Classification of Spillway (shown in Vischer et al, San Francisco,1988).
  • 28. Spillways: Functions and Classification 5 1.4 CLASSIFICATION OF SPILLWAYS Spillways have been classified according to various criteria I. According to the most prominent feature A. Ogee spillway B. Chute spillway C. Side channel spillway D. Shaft spillway E. Siphon spillway F. Straight drop or overfall spillway G. Tunnel spillway/Culvert spillway H. Labyrinth spillway I. Stepped spillway II. According to Function A. Service spillway B. Auxiliary spillway C. Fuse plug or emergency spillway III. According to Control Structure A. Gated spillway B. Ungated spillway C. Orifice of sluice spillway Vischer et al. (1988) have proposed a more comprehensive classification that seeks to include essentially all components of the spillway: inlet, regulation or control, discharge carrier, and outlet (including energy dissapators). Their classifi- cation—with minor modifications—lists the following alternatives in each com- ponent and is shown schematically in Figure 2. It would seem that if every element could be combined with all the others, (i.e., 5 ⳯ 5 ⳯ 5 ⳯ 3), 375 combinations would be possible, or 375 different types of spillways. However, several combinations are not meaningful, such as radial gate, siphon; free fall, ski jump; etc. Only about 65 combinations seem meaningful, and very few are of practical interest. REFERENCES 1. Moric, P. ‘‘Questioning the need for spillways’’, International Water Power & Dam Construction, January, 1997. 2. Mriouah, D. ‘‘Crues Importantes imprevues: cas du barrage de Oued el Makhazine all Maroc’’, Q-63, R-82 Proc. 16th ICOLD. San Francisco, June 1988.
  • 29. Chapter 1 6 3. Takasu, S.; Yamaguchi, J. ‘‘Principle for selecting type of spillway for flood control dams in Japan’’, Q-63, R-19, ibid, 1988. 4. ‘‘Seminar on Safety Evaluation of Existing Dam for Foreign Engineers – History of Dam Safety Development in the U.S.’’ USBR, 1983. 5. Vischer, D.; Rutschmann, P. ‘‘Spillway facilities – Typology and General Safety Questions’’, Q-63, R-23, Proc. 16th ICOLD:. San Francisco, June, 1988.
  • 30. 2 Spillway Design: An Overview 2.1 INTRODUCTION The object of spillway design, which involves two steps, is to provide a safe and adequate spillway structure for the lowest combined cost of the spillway and the dam. The first step in the design involves determining the type and overall size of the spillway structure to suit the anticipated requirements and conditions of the site. A detailed hydraulic and structural design of the spillway structure is the next step. This chapter is concerned with the general procedure of an overall design. An evaluation of the basic data should be the first step in the preparation of the design. This includes the topography and geology as well as flood hydrogra- phy, storage, and release requirements. The type, size, and elevation of the crest and whether it will be controlled can also be tentatively decided. Several alterna- tive arrangements might be possible and a final layout could be created on the basis of economic analysis. However, considering analyses of existing spillways could be useful in understanding trends towards the types of spillways for a given set of conditions. 2.2 ANALYSIS OF EXISTING STRUCTURES It would be of interest to analyze existing structures to see if there was a trend for adopting a particular type of spillway in a given set of condition. Semenkov (1979) analyzed more than 400 projects in terms of parameters L/H and N for the three main types of spillways: gravity spillways, chute spillways, and tunnel spillways for concrete and earth-fill dams. Here, L and H are the length and height of the dam crest respectively, and N is the power of the flow from the 7
  • 31. Chapter 2 8 spillway given by 0.0098 ⳯ Q ⳯ Hb, MW, where Q (cumec) is the discharge and Hb (m)—the difference between the upstream water level and natural river bed. The results are shown in Figure 1. In the projects with concrete dams, the spillways were mainly located within the channel portion of the river valley with any combinations of L/H and N. About 35% of spillways of concrete dams are used in combination with sluices and bottom outlets and the use of chute spillways and tunnel spillways makes up about 10% and 5% respectively. In the projects with earth-fill dams, gravity spillways were used with L/H from 8 to 1700. In the narrow valleys, gravity spillways were used when the power of the flow discharged was small. In the case of great flows, chute spillways were preferred. On wide valleys, spillway tunnels gave way to chute spillways, Figure 1 Types of spillways for concrete and earth-fill dams. T: Tunnel spillways, C: Chute spillways, G: Gravity spillways (shown in Semenkov, New Delhi, 1979).
  • 32. Spillway Design: An Overview 9 as the power of the flow discharged was more than 5000 MW. Tunnel spillways make up about a quarter of all flow-release structures of earth-fill dams. 2.3 VARIOUS ASPECTS INVOLVED IN A SPILLWAY DESIGN The following aspects are involved in the design of spillways: Hydrology Topography and geology Utility and operational aspects Constructional and structural aspects 2.3.1 Hydrology The hydrological aspects relevant to the spillway design are: Estimation of inflow design flood (IDF) Selection of spillway design flood Determination of spillway outflow discharge Determination of frequency of spillway use Estimation of inflow design flood for a given dam site is an exercise in hydrology, therefore, procedures are fairly standardized. The earlier approaches of regional flood formulae (such as Inglis, Dickens, etc.) and envelope curves have now been replaced with refined methods involving statistical analyses (flood frequency series) and numerical modeling of rainfall–runoff relationships. On the other hand, selection of the spillway design flood is a function of social, moral, and economic, as well as technological considerations. While the previous design flood–selection criteria considered factors such as dam height, storage volume, and downstream development, current practice is to select a design inflow flood on the basis of the consequences of dam failure. This is one of the most debated issues of spillway design and different countries have their own standards or procedures for selecting spillway design flood. A detailed discussion on this topic is included in the chapter, ‘‘Spillway Design Flood: Estimation and Selection’’. The spillway outflow discharge corresponding to an inflow flood is de- termined from the flood-routing analysis. At least a tentative design of the spillway—Full Reservoir Level (FRL), crest level, number of spans, and an ap- proximate discharge rating curve for the spillway—is necessary for a flood- routing analysis. The design of various elements of the spillway such as crest profile, sidewalls, energy dissapator and downstream protection are all based on spillway outflow discharge.
  • 33. Chapter 2 10 The frequency of spillway usage is determined by the run-off characteristics of the drainage area and the flood storage capacity available in the reservoir. Ordinary river flows are usually stored in a reservoir, diverted through head works, or released through outlets; therefore, the spillway may not be required to function. At diversion dams, where storage space is limited and diversion flows are relatively small compared to flood flows, a spillway is used more frequently. When the flood flows are generally restricted to a small duration and are flashy in nature, the spillways are expected to operate more frequently. The design philosophy for such spillways favors a more elaborate and fail-safe design. 2.3.2 Topography and Geology Topography and geology, with selected subsurface explorations, have greater influence on the location and type of spillway than any other factors. The class and amount of excavation, possibility of seepage and piping, value of excavated material for other purposes, possibility of scour and subsequent need for lining, location of faults, type of foundation, and bearing pressures allowed are some of the items considered. These considerations thus determine the type and location of a spillway as follows: 1. Ogee spillway: Most commonly used as the integral overflow section of a concrete or a masonry dam. 2. Chute spillway: Adopted in a site where a suitable foundation with moderate depth of excavation is available, where topography of the site permits the use of a relatively short channel, or where spillway excavation can be used economically in the dam. 3. Side channel spillway: Suitable for earth or rock-fill dams in narrow canyons and for other situations where direct overflow is not permis- sible. 4. Shaft spillway/Tunnel spillway: Used advantageously at dam sites in narrow canyons where abutments rise steeply or where a diversion tunnel or conduit is available for use as the downstream leg. 5. Siphon spillway: Used when there is a desire for an automatic operation without mechanical parts and the discharge to be passed is small. 6. Free over-fall spillway: Suitable for arch dams 7. Duck bill spillway: Used when the waterway and foundation for the spillway are limited and a curved crest-projection into the reservoir is possible. 2.3.3 Utility and Operational Aspects From the standpoint of serviceability, spillways may be defined in three broad classes as follows.
  • 34. Spillway Design: An Overview 11 Service Spillways Include any spillway that may be utilized without significant damage to the struc- ture or downstream channel. As a general rule, service spillways have paved channels and suitable energy dissipators. Limited Service and Additional Spillways Include any spillway that may be utilized infrequently for operation of the reser- voir without incurring excessive damage. Some extraordinary maintenance at infrequent intervals would be acceptable in order to reduce initial construction costs, but not to the extent of imposing significant limitations on the optimum utilization of the reservoir’s controlled storage capacity under normal operating conditions. Emergency Spillways Include any spillway, the use of which to be avoided as long as possible, used to prevent major damage to the spillway structure or to downstream areas. Emer- gency spillways may involve partial control by so-called ‘‘Fuse Plugs’’ or ‘‘Flash Boards.’’ The overall advantages and disadvantages of service, additional, and emer- gency spillways should be considered in the planning and design of a reservoir project. Besides the aforementioned, the spillways can be classified according to the control structure, namely controlled or gated crest and uncontrolled or ungated crest. Uncontrolled Crest Uncontrolled crests permit water to discharge whenever the reservoir surface is higher than the crest. The height of the dam is determined from the maximum flood required to be discharged and the necessary free board. Since the longest crest requires the least head, an economic balance may be found between length and height of spillway if the topography does not limit the length of the crest. Controlled Crest Gates may be used to control the reservoir water surface. The top of the gates is usually at the normal water-surface elevation of the reservoir; to keep the maxi- mum elevation constant, the gates are opened sufficiently to pass the floods. While an uncontrolled crest requires a dam higher than a controlled crest, an uncontrolled crest offers the following advantages: flood storage is always available, the necessity of gates and their maintenance is eliminated, and the crest has a greater ability to pass the logs and other debris without interference. An
  • 35. Chapter 2 12 uncontrolled crest requires less discharge capacity than a controlled crest for a given flood, since part of the flood is stored in order to acquire a head necessary to pass the discharge. An uncontrolled crest also becomes necessary for some dams located in distant valleys or where, for some reason, spillways are not accessible during floods. A completely controlled crest immediately passes all incoming floodwater if the flood starts when the reservoir is at maximum stage, but it also offers a means of draining the water level in anticipation of floods or allowing induced surcharge at the time of floods. A choice between a controlled and an uncontrolled spillway would require consideration of the above aspects. Spillways for Flood and Sediment Disposal While the prime objective of a spillway is disposal of floods, if designed specifi- cally, it may also serve for the disposal of sediment deposited in the reservoir. Mountainous streams with dependable flows and considerable heads favor selec- tion of run-off river plants. However, such streams carry large amount of sediment that could ultimately settle in the reservoir and reduce its capacity. In such projects, spillways can be designed to serve the dual purpose of flood disposal and sediment disposal to flush material deposited in the reservoir downstream, but these requirements are often conflicting. While flood disposal warrants a larger spillway capacity with a wider waterway, sediment disposal requires low- level spillways or bottom outlets of large capacity placed deep below the water surface. A detailed discussion on this topic is included in the chapter ‘‘Spillways for Flood and Sediment Disposal.’’ 2.3.4 Constructional and Structural Aspects River valley projects with multiple purposes are usually phased over long periods of time to suit the requirements of irrigation and power, financial allocations, and progress of rehabilitation of the project-affected population. The construction of major dams and spillways involves large quantities of excavation, earthwork, and concreting, and may be required to be constructed in stages. The flood flows in the intervening periods, diverted over partly constructed spillways, may set up undesirable flow conditions, thus resulting in damage to the adjacent structures already constructed by then. It would therefore be necessary to plan the construc- tion schedule, as well as spillway features, in such a way that the temporary passages of flow do not cause undesirable flow conditions. Hydraulic model study is the best means to visualize these effects and to evolve suitable designs. The choice of earth- and rock-fill dams is often based on the availability of material from the excavation for the spillways. In such situations, unlined rock spillways and unlined cascade spillways may be preferred over chute and side channel spillways. A detailed discussion on this is presented in the chapter ‘‘Unli- ned Rock Spillways.’’
  • 36. Spillway Design: An Overview 13 Many future dams are likely to adopt the technology of roller-compacted concrete. This method of construction is cost-effective, typically faster, and causes minimum project disruption. This technique also facilitates the provision of stepped spillways since the rolling in lifts of 30 to 60 cm favors the construction of a stepped surface as the height increases. The stepped spillways ensure energy dissipation on the flow surface itself at almost double that of an unstepped, smooth spillway. The theory and case studies on stepped spillways are discussed in the chapter, ‘‘Stepped Spillways.’’ 2.4 ECONOMIC ANALYSIS The procedure for economic analysis has been illustrated by the USBR (1960). The analysis seeks to identify an optimum combined cost of the dam-spillway combination. In determining the best combination of storage and spillway capac- ity to accommodate the selected design flood, all pertinent factors of hydrology, hydraulics, design cost, and probable damage should be considered. Such factors may be: (1) the characteristics of the flood hydrograph; (2) the damages that would result if a flood occurred without the dam; (3) the damages that would result if such a flood occurred with the dam in place; (4) the damages that would occur if the dam or spillway were breached; (5) the effects of various dam- spillway combinations on the probable increase or decrease of damages above or below the dam; (6) the relative cost of increasing the spillway capacity; and (7) the use of outlet facilities to serve more than one function, such as control of releases and control or passage of floods. The costs of dams are worked out as functions of maximum reservoir level. For a given inflow flood, an increase in the maximum reservoir level increases the height and hence, the cost of the dam. However, the flood absorption capacity of the reservoir also increases, which results in a smaller outflow discharge for thespillway—whethergatedorungated—resultinginasmallersizeofthespillway and hence, a reduction in the cost. The results are plotted as shown in Figure 2. The curves representing the combined costs of dam-spillway combinations indicate the optimum height of the dam that gives the minimum cost. However, the costs considered in the economic analysis described before only include the first cost. The analysis ought to include the probable cost of repair and maintenance of the spillway structure. Regan (1979) commented on this procedure citing examples of the spillways of Libby and Dworshak dams, United States. The initial costs of both of these structures decreased with the reduction in number of spillway spans and sluices. However, the increase in the unit discharge that contributed to an enormous damage, and necessitated huge expenditure in repairs, was not reflected in the cost of the spillway at the time of planning. The repair cost in each case was about five million dollars. Perhaps,
  • 37. Chapter 2 14 Figure 2 Comparative costs: spillway-dam combinations. A:Minimum cost: gated spill- way, B: Minimum cost: ungated spillway (shown in USBR, United States,1960). a wider spillway with undersluices, though resulting in an increased intial cost, would have avoided high-energy concentration in the discharge channel and would have substantially minimized the damage and subsequent efforts for re- pairs, if not eliminated them altogether. Admittedly, such visualization in advance requires experience and foresight on the part of the designer, and there lies the complexity of the hydraulics of high velocity flows. REFERENCES 1. Regan, R. P. Comments on the paper- Cavitation and erosion damage of sluices and stilling basins at two high-head dams- 13th ICOLD, New Delhi, 1979; Vol. V, 580. 2. Semenkov, V. M. General Report on Q 50- Large capacity outlets and spillways, 13th ICOLD, New Delhi, 1979; Vol. V, 94. 3. Design of Small Dams, United States Bureau of Reclamation. USBR, USA, 1960.
  • 38. 3 Spillway Design Flood: Estimation and Selection 3.1 INTRODUCTION The overtopping of dams causes more than a third of all dam failures. Equipment malfunctions or operational errors are sometimes to blame, but the principal cause is inadequate spillway capacity. Thus, the importance of spillway design flood cannot be over emphasized. In many cases, because the consequences of dam failure would be so severe, no significant level of failure can be tolerated, and protection should be provided up to the maximum flood levels. However, where the consequences would be less serious, the probability of slight failure would be acceptable, and the expenditure for protecting the dam can be reduced. Besides, the distinction can also be made between dam safety and works discharge capac- ity. This approach, in practical terms, leads to two design floods and their spillway discharge capacity. The Safety Check Flood This flood is often made equal to the Probable Maximum Flood (PMF). It is considered acceptable practice for the crest structure, waterway, and energy dissa- pator to be on the verge of failure, but to exhibit marginally safe performance and an accepted risk of damage without total failure. The Design Flood This flood strictly represents the inflow, which must be discharged under normal conditions with a safety margin provided by the free board. The design flood is usually taken as a percentage of PMF or is a flood with a given probability of exceeding its capacity, such as 1:100, 1:1000, etc. 15
  • 39. Chapter 3 16 Two aspects concerning the spillway design flood, estimation and selection, have been discussed here. The first falls within the responsibilities of a hydrolo- gist, the latter within those of a dam designer. 3.2 ESTIMATION OF SPILLWAY DESIGN FLOOD The estimation of spillway design flood or the inflow design flood is an exercise involving diverse disciplines of hydrology, meteorology, statistics and probabil- ity. There is a great variety of methods used around the world to determine exceptional floods and their characteristics. ICOLD (1992) groups all these meth- ods under the two main categories: Methods based mainly on flow data. Methods based mainly on rainfall data. Historical methods, empirical and regional formulas, envelope curves, and flood frequency analysis are included in the first catergory whereas rainfall-runoff anal- ysis, based on unit hydrograph and hydrologic modeling, is included in the second category. It is beyond the scope of this book to present each method thoroughly and their peculiarities, which depend on location, climate and usage, as well as the size and importance of the structure. Only an overview of the methods has been presented; refer to the bibliography for further reading on these methods. 3.3 METHODS BASED MAINLY ON FLOW DATA In ancient times, the most commonly used site–specific measurement was mark- ing the water level, still preserved in several places, from which a rough estimate of the corresponding discharge could be made along with suitable assumptions of waterway, slope, and friction. Next, the direct measurement of discharge along with water levels was taken followed by series of measurements for several more years. The following methods are based on the analysis of flow data. 3.3.1 Historical Method This method is based on the assessment of flood discharge over periods of history and determined from the water levels/marks available at sections of rivers, bridges, or buildings. Their only value is in supplementing existing hydrologic data and in comparing results obtained by other methods.
  • 40. Spillway Design Flood: Estimation and Selection 17 3.3.2 Empirical and Regional Formulas During the early stages of the development of hydrology, flood estimation was primarily carried out by using empirical relationships between the observed flood peaks and easily measured variables such as the catchment area, rainfall intensity, etc. Empirical formulas may be classified into the following three groups: 1. Formulas in which the discharge holds a simple relation with the catch- ment area: Q ⳱ f (A) (1) 2. Formulas in which the discharge is a function of the catchment area and other topographical and meteorological characteristics: Q ⳱ f (A,P) where P is the precipitation (2) 3. Formulas in which other parameters such as intensity of rainfall (I), time of concentration (tc), and return period (T) are involved: Q ⳱ f (A, I, tc, T) (3) Though simple to use, these formulas are derived from small catchments and are characterized by local and regional conditions; therefore, their use is limited. Chow (1988), Raudkivi (1979), and Garde (1998) list several such formulas. 3.3.3 Envelope Curves Based on the data of observed flood peaks in rivers located in the same region, for a number of rivers with different catchment areas, the flood peak discharges and respective catchment areas are plotted on a log-log graph and are enveloped by a smooth curve; curves given by Creager, Justin, and Hinds (1944) are examples. Francou and Rodier (1967) applied this method at a world-wide scale and proposed the formula Q/Qo ⳱ (A/Ao)1-K/10 (4) where Q ⳱ maximum flood peak (cumec) A ⳱ catchment area (sq.km) Qo ⳱ 106 (cumec) Ao ⳱ 108 (sq.km) K ⳱ regional coefficient which varies generally between 0 and 6. A graph representing this formula is given in Figure 1. It can be seen that, in the graph log Q against log A, the K equals constant lines that are envelopes of maximum observed flood peaks in hydrologically homogenous regions. These lines converge to a single point F, whose coordinates (Ao ⳱ 108 sq.km and
  • 41. Chapter 3 18 Figure 1 Francou-Rodier Envelope Curves. Qo ⳱ 106 cumec) represent the approximate total catchment surface of the earth experiencing precipitation (including lakes but excluding deserts and ice-caps) and the mean annual discharge of all rivers draining these surfaces. The equation is valid only in a flood zone whose lower limit is about 100 sq.km. Below this limit, the maximum flow peak tends to depend only on the maximum rainfall intensity alone. 3.3.4 Flood Frequency Analysis The occurrence of annual floods at a given site cannot be predicted with certainty because the magnitude of flood discharge is a random variable. Hence, statistical methods are used to predict the design flood for large structures like spillways, bridges, etc. The prediction of the design flood is made by analyzing the data of the past floods for 20 to 60 years. The data is a sample from the population, which consists of annual floods that have occurred at the site, provided that the population considered complies with the following two conditions: The population is homogeneous; for example, the flood records are not affected by dams, diversions, urbanization, etc. The characteristics of the population are stationery, that is, independent of time.
  • 42. Spillway Design Flood: Estimation and Selection 19 Two types of flood series are used by hydrologists for such predictions. The first one is the Annual Flood Series (AFS) in which the highest peak occurring every year is selected. The second series is formed by taking peaks above a certain threshold and is called Partial Duration Series (PDS). AFS is more relevant when it is required to determine risk according to the time of the year while PDS is used for estimation of flows of a low return period. Generally, the two analyses give almost the same results beyond return periods of 10 years. In the frequency analysis, a probability of occurrence has to be assigned to each flood magnitude. Assigning such a probability is known as determination of the plotting position. For this, the sample data are arranged in descending order of magnitude and rank is given to each value as 1, 2, 3, etc. If two or more observations have the same value, each one is assigned a unique rank assuming them to be different. If m is the rank and there are N observations in the series, the plotting position m/(NⳭ1) is more often used by hydrologists. Once the plotting position is assigned to each flood magnitude in the sample, the probability distribution law that the data follows is determined. The probability of ex- ceedance, p (X⬎x), is related to the return period as T ⳱ 1/p (X⬎x) (5) The most commonly used probability distribution or laws used in hydrology are: Gassian or normal, log-normal, log-Pearson type III, and Extreme value-I, or Gumbel distribution. There is, however, no satisfactory logical basis for preferring one distribution to the other and usually the one that best fits the data of that region is recommended for use. In developing countries, where long-term AFS are not available, the method of regional flood frequency analysis is useful. At present, the most used method for regional analysis is the index flood method, due to a US Geological Survey (1960). Garde (1998) gives a brief account of regional flood frequency studies carried out in India. 3.4 METHODS BASED MAINLY ON RAINFALL DATA These methods are based on the rational analysis of rainfall and run-off data and are considered more reliable for estimating floods. These methods not only give the peak discharge, but also provide the complete flood hydrograph and thereby give flood volume and a decided advantage in the design of storage reservoirs. Continuous discharge data for at least 4 to 5 rainy seasons with adequate concur- rent rainfall data are essential. In addition, rainfall data for as many rain gauge stations in and around the catchment area, including hourly rainfall data, would
  • 43. Chapter 3 20 be very valuable for assessing areal and time distribution of rainfall. For very large basins, the methods can be applied to their sub-basins with hydrologic or hydraulic routing of the resultant flows. In this connection, the definitions of the maximum flood are quite relevant and are listed next. Probable Maximum Flood (PMF) This is the flood that may be expected from the most severe combination of critical meteorological and hydrological conditions that are reasonably possible in the region. This is computed by using the Probable Maximum Storm, which is an estimate of the physical upper limit to maximum precipitation in the basin. This is obtained from transposition studies of the storms that have occurred over the region and maximizing them for the most critical atmospheric conditions. The storms are maximized to ascertain how rainfall of a particular storm could have been increased by an increase in the meteorological factors producing the storm. These are the mechanical efficiency of the storm and the moisture content of rain producing air mass involved in the storm. Standard Project Flood (SPF) This is the flood that may be expected from the most severe combination of hydrological and meteorological factors that are considered reasonably character- istic of the region and is computed by using the Standard Project Storm (SPS). While transposition of storms from outside the basin is permissible, very rare storms that are not characteristics of the region concerned are excluded from the SPS. Also, the process does not involve maximization of the factors, as done for the PMS. There are basically two methods of rainfall-runoff analysis used to derive flood hydrographs of the desired characteristics: Unit hydrograph method Hydrologic modeling; also known as Conceptual Rainfall-Runoff (CRR) model However, the first step in the analysis is the determination of PMS or SPS. 3.4.1 Development of the PMS and PMP The Probable Maximum Participation (PMP) is defined as the theoretically great- est depth of precipitation for a given duration that is physically possible over
  • 44. Spillway Design Flood: Estimation and Selection 21 a given size storm area at a particular geographic location at a certain time of a year. For each drainage basin there is a PMP, which produces a critical flood at the dam site. To select this PMP, run-off hydrographs produced by large, historic storms are examined. These storms usually constitute the greatest rainfall depths on record for the particular location or surrounding region. Such storms are fre- quently associated with significant flooding and damage. Having obtained a suita- ble severe storm database, areal-durational rainfall depths from these storms are adjusted in developing estimates of PMP. There are three basic adjustments made to the observed rainfall data: Moisture maximization Transposition Envelopment Moisture maximization is a process whereby observed precipitation is increased to a value consistent with the maximum moisture in the atmosphere for the storm location. The basic storm moisture maximization is expressed as: P P a o = W W p p storm (max) ( ) where Pa ⳱ adjusted moisture maximized precipitation Po ⳱ observed precipitation, Wp (storm) ⳱ observed precipitable water Wp (max) ⳱ maximum precipitable water Application of this adjustment results in storm rainfall depths that are considered to have reached conditions represented by the physical maximum of moisture available in the air above a basin and the rate at which wind may carry the humid air into the basin. Storm transposition involves relocating individual storm precipitation within a region considered homogeneous relative to topographic and meteorologic characteristics deemed significant to that storm. Since each location of interest has not likely experienced the number of severe storms necessary for PMP devel- opment, storm transposition becomes an important tool for providing additional data at a particular site. Storm envelopment involves the selection of the greatest likely value from a set of data. This step becomes a requirement due to the lack of a uniform storm database for every duration, area, location, and season of interest. For more details, refer to the excellent treatment of the subject by the World Meterologic Organisation (1986), Cudworth (1989), and Myers (1967). Once the PMP depth has been calculated, it must be distributed chronologi- cally into a logical storm sequence. Studies of rainfall occurrences have shown
  • 45. Chapter 3 22 that the variation of rainfall depths in a storm is random. However, conservative considerations have been developed for time wise distribution of rainfall depths, which must vary from zero, at the beginning and end of the storm, to a maximum at some intermediate time increment, generally near the mid-point of the storm. Data available from national weather services or meteorological departments in respect to time distribution of rainfall data, as well as guide lines offered by USBR (1987), may prove to be helpful for further reading. 3.4.2 Unit Hydrograph Method Unit hydrograph is defined as the hydrograph of direct run-off (excluding ground water) from a given basin resulting from 1 inch of excess rainfall, generated uniformly over the basin area at a uniform rate during a specified time period (duration) such as 1 hour, 2 hour, etc. Thus, a 6 hour unit hydrograph is the rainfall excess generated at 1/6 inch per hour. A unit hydrograph thus represents the integrated effects of all the basin characteristics such as drainage area, shape, stream channel pattern, channel capacities, land slope. and other physical factors. The theory of unit hydrograph assumes that excess rainfall is distributed uniformly over time and over the basin. A direct run-off hydrograph resulting from an isolated, intense, short dura- tion storm, of nearly uniform distribution in space and time, is the most desirable to satisfy the above assumptions in the theory. If stream flow records are not available, synthetic unit hydrograph can be obtained from known physical charac- teristics of the basin. Snyder (1938) has developed relationships for synthetic unit hydrographs. Compiling a design hydrograph from a unit hydrograph of a specified dura- tion involves, superimposing on the unit hydrograph ordinates, the effect of rain- fall excess of the design storm. Various segments of the storm are superimposed and added to obtain the design flood hydrograph. For large catchments, unit hydrographs are worked out for several sub- areas, rainfall excess is applied to the unit hydrographs of each area and flooding from each sub-area is routed to the outlet point of the whole catchment. Several program packages are available for the combined calculations of rainfall excess, unit hydrograph transfer and river routing, which facilitate compu- tations involved in the process. The most preferred is the HEC-1 flood hydrograph package, developed by the US Army Corps of Engineers (1990). 3.4.3 Hydrologic Modelling Generalized approaches to model water resources systems also exist. These models are classified into two categories: deterministic and stochastic. Determin- istic models are those whose operational characteristics are in terms of known
  • 46. Spillway Design Flood: Estimation and Selection 23 physical laws or empirical relationships, while stochastic models are expressed by probability functions. Both of these model types play important roles in hydro- logic simulation and analysis. However, a deterministic model is more readily adaptable to the examination of land use changes and provides more insight into the physical processes of the hydrologic cycle. Deterministic models are further classified as empirical models, conceptual models, and physical distribution models. Relationships developed for physical processes without significant impor- tance to constituents are known as empirical relationships. Models based on such relationships are called empirical models. Such models usually depend on estab- lishing a relationship between input and output, directly or indirectly, using a few parameters; as for example, the rainfall-runoff function. Within the range of calibration data, such models may be successful owing to an implied mathematical structure inherent in the analysis. However, in extrapolating beyond the range of calibration, the physical link is weakened and the prediction then relies on mathematical technique alone. Since no physical process is simulated, such models cannot be used to predict the effect of a future changes in land use patterns. Conceptual models are based on some consideration of the physical pro- cesses in the catchment, as for example, an elaborate Conceptual Rainfall-Runoff (CRR) model. CRR models comprise a series of functions that mimic the water movement within a basin such as: infiltration, overland flow, sub-surface flow, and evapotranspiration. Important features of CRR models include keeping track of the present state of moisture conditions of the watershed and modeling some of the dominant non-linearity of the system such as those associated with satura- tion of soil mass. The major data required for CRR models include: stream flow data (such as hourly gauge-discharge data), channel configurations, rating curves, particulars of flow diversion, hourly and daily data of precipitation, evaporation, evapotranspiration, and basin characteristics such as area, travel-time in reaches, soil types, etc. Models based on mathematical relationships using the basic equations gov- erning the system are called physically based models. Such models simulate the complete regime and provide multiple outputs. These models are spatially distributed as the equations formed involve one or more space coordinates. Such models require large data and computation time. Stochastic models are based on the premise that all hydrological processes are more or less stochastic in nature. If the available record (i.e., a time series) is of sufficient length to be considered as a representative sample, the statistical parameters derived from it will enable formulation of a reliable stochastic model. The data generated by this model will not be qualitatively better than the historical observed data. The major advantage is that many combinations of patterns of data sequences can be synthetically generated for a length longer than the ob- served data.
  • 47. Chapter 3 24 Once a hydrological model is selected, it needs to be calibrated and calibra- tion is invariably data demanding. The models use mathematical equations con- taining parameters representing different phases of the hydrological cycle. A general rule in the case of CRR models is that for calibration, about 5 years of continuously recorded hydrometeorological data should be used. Once the model is satisfactorily calibrated it needs to be further tested for its accuracy. This time, a new set of data is required called validation data, obviously for a different time period than used for calibration. CRR models can be broadly divided into explicit soil moisture accounting (ESMA) and implicit soil moisture accounting (ISMA). Some of the well-known CRR models under ESMA are Stanford Watershed Model (SWM), Kentucky Water Shed Model (KWM), and Streamflow Synthesis and Reservoir Regulation (SSARR); whereas the Tank model falls under ISMA. The self-calibrating version of KWM is the OPSET (for evaluation of Optimum SET of parameters) model written in Fortran. For detailed information on various models, refer to Singh (1982) and (1989). 3.4.4 Gradex Method The most recently developed method in France is the method of Gradient of Extreme values or Gradex method. It involves a major simplification of the rain- fall-runoff process and identifying the most pertinent characteristics dealt with in a statistical model. One of the basic assumptions of the Gradex method is that the cumulative distribution functions of the areal rainfall in the catchment hold within a very large range of probabilities. The Gradex method may be used for the basins whose base time or time of concentration is smaller than about three days. The method requires the availability of flood records for10 years to derive the quantities relative to return periods of 20 to 50 years. This method cannot be used in areas where storm events may be of cyclonic type which are not amenable to a single cumulative distribution function. For a detailed discussion on this method, see Duband et al. (1988). 3.5 FLOOD ESTIMATION METHODS: CRITICAL ANALYSIS Basic flood estimation methods with comments on application were covered ear- lier. While there is a need for consistent standards, there is no single method or methods to embrace all factors, particularly where data are scarce, where flows are highly variable, and where rare meteorological conditions can produce excep- tional storms. For large dams with major consequences of failure, the design flood annual exceedance probability is generally in the range of 1:1000 to 1:100000. Such probabilities are well outside the range of the limited data bank
  • 48. Spillway Design Flood: Estimation and Selection 25 available to develop and calibrate any flood estimation method. It would be practicable to use a combination of frequency analysis and hydrological modeling to obtain a wide range of flows expected and to determine the most suitable value considering relevant factors that characterize the basin as a whole. The discussion on flood estimation is concluded with the case study of the Sardar Sarovar dam where various approaches were used for the estimation of PMF. 3.5.1 Estimation of Design Flood for the Sardar Sarovar Dam on River Narmada, India River Narmada in Central India flows almost West-Southwest over 1300 km to join the Arabian Sea and is the largest west flowing river in India. The river’s basin has an elongated shape with a maximum length of 953 km (East to West), a maximum width of 234 km (North to South), and is oriented almost parallel to the storm tracks originating from the Bay of Bengal. The storm and river flows have, at times, synchronized to cause record floods with disproportionately large peak discharges. The Sardar Sarovar dam forms a terminal reservoir at 1153 km from the source and intercepts an area of about 88000 sq.km. The climate of the basin is humid and tropical. The normal annual rainfall for the basin is 1178 mm, nearly 90% of that occurring from June to October. The river has 41 tributaries, of which 22 are on the left bank and 19 are on the right bank. Approximately, 75% of the basin area is covered by either the black soils or medium black soils whose infiltration rates are quite low. The estimation of PMF is based on the following approaches: I. Flood frequency analysis II. Hydrological modelling using A. SSARR B. OPSET coupled with Muskingum Kinematic routings C. HEC-1 model based on Clark’s instantaneous unit hydrograph Flood Frequency Analysis The observed stream flow data at the Garudeswar gauge site, 11.3 km downstream of Sardar Sarovar dam, for the period 1948 to 1980 were subjected to statistical analysis for the purpose of developing distributional models. The flood discharges in the series varied from 10,364 cumec to 69,405 cumec. Figure 2 shows the relationship between the discharge (Q) and the return period (T) using LP-III and Gumbel distribution under AFS as well as the relationship obtained with PDS approach.
  • 49. Chapter 3 26 Figure 2 Flood frequency analysis of flood data for Narmada at Garudeswar. ● Observed ᎏᎏᎏ LP III ᎏ 䡠 ᎏ P.D.S – – – – Gumbel In this particular case, LP-III distribution proved to be a better fit than Gumbel distribution. Comparison between flood discharges estimated for differ- ent return periods are shown below. Return Estimated flood, cumec Period, AFS PDS Years Gumbel LP-III 100 73,260 84,020 71,380 500 90,710 112,430 92,850 1000 98,210 124,510 101,660 10000 123,130 154,030 130,880 Hydrological modeling The entire basin was divided into 20 sub-basins and the PMP adopted for the initial studies was based on an August 1973 storm using a maximization factor of 1.35. The SSARR model gave a peak flood of about 102,874 cumec whereas OPSET model gave a peak flood of about 112,000 cumec. In the subse- quent studies, in addition to the insitu storm over the basin, storms over the
  • 50. Spillway Design Flood: Estimation and Selection 27 adjacent basins were also considered and transposed. A July 1927 storm with a maximization factor of 1.13 (Storm A) and the August (1973) storm with maximi- zation factor of 1.59 (Storm B) were adopted with OPSET model and Muskingum and Kinematic routing procedures. The summary of results is given below: Storm A Storm B Muskingum Kinematic Muskingum Kinematic 165,650 170,990 144,420 146,940 The unit hydrographs for 28 sub-basins were derived and routed by Muskin- gum method. For this, the 1973 flood with a maximization factor of 1.35 and the 1927 flood from the adjacent basin, which was transposed, with a maximization factor of 1.13 were used. The PMF derived from the above analysis was assumed to be preceded by a flood of a 25-year return period–a 1968 flood observed with a peak of about 58000 cumec. The peak values obtained were 133,480 cumec and 174,290 cumec, respectively. For further details, see Desai et al. (1984). It would be interesting to compare the above values with those obtained by application of various envelope curves for flood estimation. Some of the results are given below: Envelope curve Maximum flood (cumec) Creager, Justin and Hinds 58,000 Kanvar Sen and Karpov 41,060 (for Northern and Central Indian rivers) Francou and Rodier 59,950 (with highest value of 6 for the regional coefficient K) 3.6 SELECTION OF SPILLWAY DESIGN FLOOD While the estimation of spillway design flood is an exercise in hydrology and related disciplines, selection of Spillway Design Flood (SDF) involves social, moral, economical, as well as technological judgment. In the cases, where clearly defined criteria or methodologies do not exist, selection of the SDF may prove to be difficult and controversial. While too small a spillway capacity involves a high risk of total failure of the dam by overtopping, an excessively large capacity will involve higher cost and in addition, endanger the lives and properties of downstream inhabitants due
  • 51. Chapter 3 28 to erroneous reservoir operation (the so-called man-made flood) or due to the malfunction of spillway gates, allowing discharges in excess of the carrying ca- pacity of the downstream valley. Graham (2000) mentions that while modifica- tions to existing dams can reduce economic losses from dam failure, they can also lead to economic losses due to large spillway flows in non-failure events. Thus, selection of the design flood is governed not only by the degree of risk judged acceptable in the event of it being exceeded but also during normal periods. 3.6.1 Economic Risk Analysis (ERA) The earlier approaches to determining the design flood relied heavily on the economic approach, balancing the cost of providing protection against losses that would occur when protection is insufficient. Smith (1993) has illustrated an example of selection of the design flood frequency by incorporating in the analysis the parameters of annual cost, annual damage, and the B/C (benefit to cost) ratio. Annual cost is worked out considering the expected life of the project and also includes interest, amortization, operation, maintenance, etc. Average annual dam- age (natural) represents the cost of replacing lost goods and restoring services, government expenses for flood fighting, evacuation, etc., had the dam not been built. Conceptually, the average annual damage may be thought of as the damage in 100 years divided by 100. With the construction of a dam, the extent and frequency of damage will be reduced. The damage that still occurs is referred to as the residual damage. The benefit derived from the dam is equal to the value of the damage prevented or the original damage minus the residual damage. The benefits and costs corresponding to various frequencies of floods are calculated and the B/C ratios are marked against those frequencies as shown in Figure 3. The analysis thus helps in selecting the most economic proposal. The methods proposed by Fahlbusch (1979), Von Thun (1985), and Afshar and Marino (1990) are based on Economic Risk Analysis (ERA). The basic idea Figure 3 Optimum Design Flood Frequency by Economic Analysis (after Smith 1993).
  • 52. Spillway Design Flood: Estimation and Selection 29 of economic risk analysis as reported by Bouvard (1988) is in optimizing the maximum flow Qo that has to be transferred downstream without endangering the dam. A flow Q higher than Qo will lead to overtopping, the probability of the occurring in any year being 兰ⴥ Qo ␳(q)dq (6) In which p(q) is the probability density of the flow-function considered. The expected cost of overtopping over a long period is given by A a p q dq Qo ( ) ∞ ∫ (7) where a ⳱ Discount rate A ⳱ Direct and indirect cost of overtopping to be evaluated in each case Floods above Qo would overtop and destroy an earth dam, empty the reservoir, and release downstream a devastating flood of a size determined by the reservoir capacity. Parameter A may be considered independent of the flood discharge be- cause the downstream surge wave from a large reservoir will be produced essen- tially by the release of the stored water. This considerably simplifies the equation and enables the expected value of C, the cost of the damage to be written as C = A a F Q ( ) 0 (8) Where F(Qo) is the total probability of occurrence of a flow greater than Qo — in a sense the reciprocal of the return period—the function decreases as Qo increases. Adding the cost of the spillway to the expected value of the damage caused by dam failure yields a plot of the total cost. This passes through a minimum, which in theory corresponds to the optimum cost of the spillway and the magni- tude of Q. 3.6.2 Comments on ERA A comprehensive ERA investigation was conducted for the French earth dam at Serre-Poncon. The analysis revealed some practical difficulties in choosing a range of values of A due to the fact that the resulting optimum was extremely flat. The total cost defined above rose only by 7% when Qo increased by 40% from 2900 to 4000 cumec; while at the same time, increase in the flow consider- ably altered the safety situation. It was considered that the expression for A ought to have reflected an extremely important consideration: the equivalent in financial terms of the loss of life resulting from dam failure and an agreed monetary value for each life lost. There is, however, general reluctance among practicing